Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, in the sequence 3, 7, 11, 15, the common difference is 4.

Front

How do you find the three arithmetic means between two numbers?

Back

To find the three arithmetic means between two numbers, first calculate the common difference by dividing the difference between the two numbers by the number of intervals (in this case, 4). Then, add the common difference successively to the first number.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution: about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.73% falls within three standard deviations.

Front

How do you calculate the sum of an arithmetic series?

Back

The sum of an arithmetic series can be calculated using the formula: S_n = n/2 * (a + l), where S_n is the sum, n is the number of terms, a is the first term, and l is the last term.

Front

What is the mean of a data set?

Back

The mean is the average of a data set, calculated by adding all the values together and dividing by the number of values.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Front

How do you interpret a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean. A z-score of 0 means the value is exactly at the mean, while a positive z-score indicates a value above the mean and a negative z-score indicates a value below the mean.

Front

What is a normally distributed data set?

Back

A normally distributed data set is one that follows a bell-shaped curve, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

Front

How do you find the percentage of values within a certain range in a normal distribution?

Back

To find the percentage of values within a certain range in a normal distribution, you can use the empirical rule or z-scores to determine how many standard deviations the range is from the mean.

Front

What is the formula for finding the nth term of an arithmetic sequence?

Back

The nth term of an arithmetic sequence can be found using the formula: a_n = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number.